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In the third century BC, Greek mathematician and astronomer

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In the third century BC, Greek mathematician and astronomer  [#permalink]

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New post 05 Mar 2018, 05:47
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Question Stats:

59% (01:31) correct 41% (01:38) wrong based on 17 sessions

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In the third century BC, Greek mathematician and astronomer Eratosthenes calculated the circumference of the Earth to be 252,000 stadia. The stadion (plural: stadia) was a unit of length used in ancient Greece and the value of 1 stadion in terms of later units of length has been the subject of much debate. One belief is that 1 stadion is equivalent to 157.5 metres while another is that 1 stadion equals 185 metres. If the circumference of the Earth is now known to be 24,902 miles (where 1 mile is approximately 1.61 kilometres), depending upon the chosen equivalent measure of a stadion, the error in Erastothenes’ calculation is the closest to

(A) 1% or 16%

(B) 15% or 75%

(C) 84% or 99%

(D) 523% or 631%

(E) 98896% or 116181%

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In the third century BC, Greek mathematician and astronomer  [#permalink]

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New post 05 Mar 2018, 13:46
This problems requires using approximations. First set up the calculation as follows using 1 stadia = 157.5m

24902 mi * (1.61km/1 mi) * (1000m/1km) * (1 stadia/157.5m)

Notice that if you multiply 1.61 by 100 it is 161. This can be canceled out with 157.5 because we are using approximations. After canceling we get:

24902 * 10 = 249020 (the 1000m became 10 because we multiplied 1.61 by 100)

Eratosthenes estimated 252,000 so his error was 3000/249000 which is about 1%. A is correct because none of the other answers are close to 1%.

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In the third century BC, Greek mathematician and astronomer &nbs [#permalink] 05 Mar 2018, 13:46
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